If you just have a single small sample for the one district (rather than several small samples from one district) then a confidence interval will be very wide. This is pushing the data to do something it was not design to do. With the SLEAC classifier we classify (low, moderate, high) based on our thesholds. This requires a lot less data to do than to create an estimate with a usefully narrow confidence interval.
If (e.g) you have thresholds at 20% and 50% so that:
Low : < 20%
Moderate : 20% - 50%
High : > 50%
and have n = 36 and 12 covered cases you would report a moderate coverage classification. It is simple and quite error free if there are not a very large number of SAM cases in the district.
A 95% CI might be:
p = 12 / 26 = 33.33%
SE = sqrt((0.3333 * (1 - 0.3333)) / 36) = 0.0786
LCL = 0.3333 - 1.96 * 0.0786 = 0.1792
UCL = 0.3333 + 1.96 * 0.0786 = 0.4874
That's 95% CI = 17.9% - 48.7%. We're no longer very sure that it is moderate.
We can try to fix this by applying a finite population correction. If we assume that there were 130 cases of SAM in the population at the time of the survey (we can get this as population * prevalence) then:
p = 12 / 26 = 33.33%
SE = sqrt((0.3333 * (1 - 0.3333)) / 36) * sqrt((130 - 36) / (130 - 1))
SE = 0.0671
LCL = 0.3333 - 1.96 * 0.0671 = 0.2018
UCL = 0.3333 + 1.96 * 0.0671 = 0.4448
We are now pretty confident of our moderate classification but (looking at the 95% CI) we do not have a great deal more information. The SLEAC classifier says "between 20% and 50%" and the estime with 95% CI tells us "its between about 20% and 45%".
The best thing to do (IMO) is to take the SLEAC classification and forget estimation.
If you have many small sampled (e.g. one per clinic catchment area or one per district) then the samples can be pooled and an overall estimate and 95% CI calculated.
I hope this is of some use.